I've had a new Jeep Cherokee for about 6 months. We thought that the initial strong new car smell would dissipate in a few weeks. It has reduced in strength but it is still so strong that my family cannot take a ride without keeping windows down. It is terrible in a hot climate to have to keep windows down and not use air conditioning in a new car. I've had many Jeeps before, but have never had this serious problem.
Out gassing and individual sensitivity to it, that is particular chemicals/materials in the manufacturing process. You get that issue also in new homes and particularly furniture and furnishing also.
But it all depends on on what particular chemicals/materials are involved.
A vehicle is a very enclosed space. When you add heat in as in your area I would guess that accelerates the out gassing issue. With the vehicle closed up there is no where to out gas.
* Have you tried to keep the recirculation OFF when the air is on as that will bring in fresh outside air. Leave your 2 rear windows open a crack and you can get some fresh air flow in and out to rid the out gassing through the window cracks.
With recirculation on you are allowing the vehicle to remain closed up with no new air added.
* If possible leaving the windows down when parked can help dissipate the problem over time. But being sealed up will slow the process.
Now I usually get that "new" car smell for a year. I am perhaps lucky that I am rarely if ever affected by this issue. My wife is at times and when we drove 300 miles home from picking up our Cherokee I did leave the rear windows open at several points to air the vehicle out though it was not bad for her or me. That was in December Northern Illinois.
Its a highly individual issue and the key is plenty of fresh air or a good circulation of fresh air through the vehicle. That is in and out flow.